deletions | additions       diff --git a/develop_ode.tex b/develop_ode.tex  index 8dce1d7..f358302 100644  --- a/develop_ode.tex  +++ b/develop_ode.tex 
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\end{equation}  This gives:  \begin{equation}\label{eqn:psi}  \psi = \atan{\frac{\omega}{z}} \arctan{\frac{\omega}{z}}  - \frac{\rm{d}\omega}{\rm{d}z}\ \arctan{\frac{\rm{d}\omega}{\rm{d}z}}\  . \end{equation}  Inserting equation~\ref{eqn:rho} and \ref{eqn:v0} into eqn.~\ref{eqn:4}, we arrive at an ordinary differential equation, that describes the functional form of the shape of the shock front:  \begin{equation}